Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1510.07972

A Relativistic Symmetrical Interpretation of the Dirac Equation in (1+1) Dimensions

Michael B. Heaney

Published Oct 25, 2015• 0 citations
arXivHTMLPDF

Abstract

This paper presents a new Relativistic Symmetrical Interpretation (RSI) of the Dirac equation in (1+1)D which postulates: quantum mechanics is intrinsically time-symmetric, with no arrow of time; the fundamental objects of quantum mechanics are transitions; a transition is fully described by a complex transition amplitude density with specified initial and final boundary conditions; and transition amplitude densities never collapse. This RSI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein's bubble experiment with a spin-$\frac{1}{2}$ particle. This RSI can predict the future and retrodict the past, has no zitterbewegung, resolves some inconsistencies of the CI, and eliminates some of the conceptual problems of the CI.

DOI
10.48550/arxiv.1510.07972

Related papers

A symmetrical interpretation of the Klein-Gordon equation

Michael B. Heaney, See Profile

Abstract. This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum me-chanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some in-consistencies of the CI, and gives intuitive explanations of some previously mysterious quantum effects. 1.

•Jan 1, 2013•9 citations

The Dirac equation without zitterbewegung

Michael B. Heaney

This paper presents a relativistic symmetrical interpretation of the Dirac equation in 1+1 dimensions which predicts no zitterbewegung for a free spin-1/2 particle. This could resolve the longstanding puzzle of zitterbewegung in relativistic quantum mechanics, and help clarify the physical meaning of the zitterbewegung currently under investigation in many-particle systems. Together with an earlier paper describing a relativistic symmetrical interpretation of the Klein-Gordon equation \cite{Heaney1}, this new interpretation resolves some inconsistencies in the conventional interpretations of both equations. This new interpretation also makes several experimental predictions that differ from the conventional interpretation of the Dirac equation.

arXiv:1410.5418•Oct 19, 2014•0 citations

The Dirac Equation: Resonance Geometry and Relativistic Quantum Identity

Young, Charles

This paper presents a geometric reinterpretation of the Dirac equation within the Dimensional Evolution (DE) framework. Without modifying the mathematical structure or empirical predictions of relativistic quantum mechanics, the Dirac equation is reformulated as a constraint on relativistic identity formation rather than as a purely kinematic wave equation. In this interpretation, the Dirac spinor encodes internal resonance structure required for relativistic coherence, while gamma matrices act as directional collapse operators mediating between internal geometry and spacetime constraints. The intrinsic doubling of solutions is explained as a structural duality between verse-domain localization and inverse-domain harmonic support, providing a physical account of antimatter without violating CPT symmetry or energy positivity. Spin, Zitterbewegung, and relativistic measurement are reinterpreted as consequences of resonance geometry rather than unexplained algebraic features. Measurement and localization are treated as local geometric stabilization processes consistent with Lorentz covariance, extending the collapse-geometry account developed in DE-SP6 (Mott) to relativistic systems. This work is interpretive and foundational in scope. It preserves full compatibility with quantum field theory and established relativistic quantum mechanics while clarifying the physical meaning of the Dirac equation’s most enigmatic structures. --- Project website: https://de-theory.com This work is part of the Dimensional Evolution research program. Additional materials, updates, and contact information will be made available via the project website as the work expands.

•Dec 18, 2025•0 citations

On the Complementary Wave Interpretation of the Dirac Equation

D.L. Bulathsinghala, K.A.I.L. Wijewardena Gamalath

The Dirac equation consistent with the principles of quantum mechanics and the special theory of relativity, introduces a set of matrices combined with the wave function of a particle in motion to give rise to the relativistic energy-momentum relation. In this paper a new hypothesis, the wave function of a particle in motion is associated with a pair of complementary waves is proposed. This hypothesis gives rise to the same relativistic energy-momentum relation and achieves results identical to those of Dirac. Additionally, both the energy-time and momentum-position uncertainty relations are derived from the complementary wave interpretation. How the complementary wave interpretation of the Dirac equation is related to the time-arrow and the four-vectors are also presented.

International Letters of Chemistry Physics and Astronomy•May 19, 2013•0 citations

A symmetrical theory of nonrelativistic quantum mechanics

Michael B. Heaney

This paper presents a new Symmetrical Theory (ST) of nonrelativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This new ST is compared to the Conventional Theory (CT) of nonrelativistic quantum mechanics for the analysis of a beam-splitter experiment. The ST makes several experimentally testable predictions that differ from the CT, which can be checked using existing technology. The ST also solves one part of the CT measurement problem, and resolves some of the paradoxes of the CT. This nonrelativistic ST is the low energy limit of a relativistic ST presented in an earlier paper \cite{Heaney1}.

arXiv:1310.5348•Oct 20, 2013•5 citations

Visualizations and Analyses of Quantum Behavior, Spacetime Curvature, and Metric Relationships in Relativistic Physics

Mardame Pangihutan Sinaga, Dolfie Paulus Pandara, Ukta Indra Nyuswantoro +2 more

This study aims to investigate essential concepts in quantum mechanics and theoretical physics, with an emphasis on the 1+1 dimension. We examine the Dirac equation for relativistic spin-1/2 particles, the Time-Dependent Schrödinger Equation in 1+1 spacetime with flat conformal metric, and connect them to the Dirac equation. Additionally, we explore the Alcubierre Metric related to warp drive, particle modeling in a harmonic potential using the Schrödinger Equation, and the Gödel Metric Solution to depict the peculiarities of spacetime. The research aims to deepen the understanding of these concepts, identify theoretical implications, and their potential applications. This research aims to enhance the understanding of fundamental physics, assist in the development of future technologies, and provide deeper insights into the universe. Its benefits lie in contributing to theoretical understanding in physics, which can spark the development of new theories. This study is limited to physics concepts in the 1+1 dimensions, without empirical experiments or practical applications. The primary focus is on the theoretical analysis of these concepts. The results of this research have potential theoretical implications in understanding basic physics and spacetime phenomena. The simplification and connections between these concepts can aid in the development of new theories in theoretical physics. The uniqueness of this research lies in its integrative approach to quantum mechanics and theoretical physics concepts in the 1+1 dimension, which may not have been extensively explored previously. Through this research, we have investigated several key concepts in quantum mechanics and theoretical physics in the 1+1 dimension. These findings can make a significant contribution to our understanding of the universe and the potential development of new theories in physics.

Jurnal Neutrino Jurnal Fisika dan Aplikasinya•Nov 2, 2023•0 citations
This paper presents a new Relativistic Symmetrical Interpretation (RSI) of the Dirac equation in (1+1)D which postulates: quantum mechanics is intrinsically time-symmetric, with no arrow of time; the fundamental objects of quantum mechanics are transitions; a transition is fully described by a complex transition amplitude density with specified initial and final boundary conditions; and transition amplitude densities never collapse. This RSI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein's bubble experiment with a spin-12\frac{1}{2}21​ particle. This RSI can predict the future and retrodict the past, has no zitterbewegung, resolves some inconsistencies of the CI, and eliminates some of the conceptual problems of the CI.
Abstract. This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum me-chanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some in-consistencies of the CI, and gives intuitive explanations of some previously mysterious quantum effects. 1.
This paper presents a relativistic symmetrical interpretation of the Dirac equation in 1+1 dimensions which predicts no zitterbewegung for a free spin-1/2 particle. This could resolve the longstanding puzzle of zitterbewegung in relativistic quantum mechanics, and help clarify the physical meaning of the zitterbewegung currently under investigation in many-particle systems. Together with an earlier paper describing a relativistic symmetrical interpretation of the Klein-Gordon equation \cite{Heaney1}, this new interpretation resolves some inconsistencies in the conventional interpretations of both equations. This new interpretation also makes several experimental predictions that differ from the conventional interpretation of the Dirac equation.
This paper presents a geometric reinterpretation of the Dirac equation within the Dimensional Evolution (DE) framework. Without modifying the mathematical structure or empirical predictions of relativistic quantum mechanics, the Dirac equation is reformulated as a constraint on relativistic identity formation rather than as a purely kinematic wave equation. In this interpretation, the Dirac spinor encodes internal resonance structure required for relativistic coherence, while gamma matrices act as directional collapse operators mediating between internal geometry and spacetime constraints. The intrinsic doubling of solutions is explained as a structural duality between verse-domain localization and inverse-domain harmonic support, providing a physical account of antimatter without violating CPT symmetry or energy positivity. Spin, Zitterbewegung, and relativistic measurement are reinterpreted as consequences of resonance geometry rather than unexplained algebraic features. Measurement and localization are treated as local geometric stabilization processes consistent with Lorentz covariance, extending the collapse-geometry account developed in DE-SP6 (Mott) to relativistic systems. This work is interpretive and foundational in scope. It preserves full compatibility with quantum field theory and established relativistic quantum mechanics while clarifying the physical meaning of the Dirac equation’s most enigmatic structures. --- Project website: https://de-theory.com This work is part of the Dimensional Evolution research program. Additional materials, updates, and contact information will be made available via the project website as the work expands.
The Dirac equation consistent with the principles of quantum mechanics and the special theory of relativity, introduces a set of matrices combined with the wave function of a particle in motion to give rise to the relativistic energy-momentum relation. In this paper a new hypothesis, the wave function of a particle in motion is associated with a pair of complementary waves is proposed. This hypothesis gives rise to the same relativistic energy-momentum relation and achieves results identical to those of Dirac. Additionally, both the energy-time and momentum-position uncertainty relations are derived from the complementary wave interpretation. How the complementary wave interpretation of the Dirac equation is related to the time-arrow and the four-vectors are also presented.
This paper presents a new Symmetrical Theory (ST) of nonrelativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This new ST is compared to the Conventional Theory (CT) of nonrelativistic quantum mechanics for the analysis of a beam-splitter experiment. The ST makes several experimentally testable predictions that differ from the CT, which can be checked using existing technology. The ST also solves one part of the CT measurement problem, and resolves some of the paradoxes of the CT. This nonrelativistic ST is the low energy limit of a relativistic ST presented in an earlier paper \cite{Heaney1}.
This study aims to investigate essential concepts in quantum mechanics and theoretical physics, with an emphasis on the 1+1 dimension. We examine the Dirac equation for relativistic spin-1/2 particles, the Time-Dependent Schrödinger Equation in 1+1 spacetime with flat conformal metric, and connect them to the Dirac equation. Additionally, we explore the Alcubierre Metric related to warp drive, particle modeling in a harmonic potential using the Schrödinger Equation, and the Gödel Metric Solution to depict the peculiarities of spacetime. The research aims to deepen the understanding of these concepts, identify theoretical implications, and their potential applications. This research aims to enhance the understanding of fundamental physics, assist in the development of future technologies, and provide deeper insights into the universe. Its benefits lie in contributing to theoretical understanding in physics, which can spark the development of new theories. This study is limited to physics concepts in the 1+1 dimensions, without empirical experiments or practical applications. The primary focus is on the theoretical analysis of these concepts. The results of this research have potential theoretical implications in understanding basic physics and spacetime phenomena. The simplification and connections between these concepts can aid in the development of new theories in theoretical physics. The uniqueness of this research lies in its integrative approach to quantum mechanics and theoretical physics concepts in the 1+1 dimension, which may not have been extensively explored previously. Through this research, we have investigated several key concepts in quantum mechanics and theoretical physics in the 1+1 dimension. These findings can make a significant contribution to our understanding of the universe and the potential development of new theories in physics.